### Abstract

Approximated equations have been constructed to describe the temperature (T) dependence of the molar volumes (V) of fcc solid metals (Ag, Al, Au, Cu, Ir, Ni, Pb, Pd, Pt, and Rh) and their liquids below and above their melting points at standard pressure of 1 bar from zero Kelvin. Below the melting point, the following new approximated equation is suggested for both the solid and liquid metals: V = a + b * T (to the power of n), where a, b, and n are semi-empirical parameters (at n larger than 1; this equation obeys the boundary condition that the thermal expansion coefficient becomes zero at T = 0 K). This approximated equation reproduces the measured molar volume of solids from zero Kelvin to melting point with an accuracy of 0.2 % or better. As a compromise, the derivative of this equation reproduces the measured thermal expansion coefficient of solids only with an accuracy 10 % or better and only above 100 K. Above the melting point, the following well-known equation is used for both liquid and solid phases: V = c + d * T, where c and d are semi-empirical parameters. This equation implies that the thermal expansion coefficient above the melting point has an approximately constant value. It is found that the volume change upon melting extrapolated to zero K is about 58 % of that at the melting point for all the 10 fcc metals. The tabulated 4 equations (below and above the melting point/for fcc and liquid states) are provided for each of the 10 fcc metals. These equations will be useful for estimating phase equilibria of nano-materials.

Original language | English |
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Pages (from-to) | 678-687 |

Number of pages | 10 |

Journal | Journal of Materials Science |

Volume | 50 |

Issue number | 2 |

DOIs | |

Publication status | Published - Nov 22 2014 |

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### ASJC Scopus subject areas

- Materials Science(all)
- Mechanics of Materials
- Mechanical Engineering

### Cite this

**Approximated equations for molar volumes of pure solid fcc metals and their liquids from zero Kelvin to above their melting points at standard pressure.** / Kaptay, G.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Approximated equations for molar volumes of pure solid fcc metals and their liquids from zero Kelvin to above their melting points at standard pressure

AU - Kaptay, G.

PY - 2014/11/22

Y1 - 2014/11/22

N2 - Approximated equations have been constructed to describe the temperature (T) dependence of the molar volumes (V) of fcc solid metals (Ag, Al, Au, Cu, Ir, Ni, Pb, Pd, Pt, and Rh) and their liquids below and above their melting points at standard pressure of 1 bar from zero Kelvin. Below the melting point, the following new approximated equation is suggested for both the solid and liquid metals: V = a + b * T (to the power of n), where a, b, and n are semi-empirical parameters (at n larger than 1; this equation obeys the boundary condition that the thermal expansion coefficient becomes zero at T = 0 K). This approximated equation reproduces the measured molar volume of solids from zero Kelvin to melting point with an accuracy of 0.2 % or better. As a compromise, the derivative of this equation reproduces the measured thermal expansion coefficient of solids only with an accuracy 10 % or better and only above 100 K. Above the melting point, the following well-known equation is used for both liquid and solid phases: V = c + d * T, where c and d are semi-empirical parameters. This equation implies that the thermal expansion coefficient above the melting point has an approximately constant value. It is found that the volume change upon melting extrapolated to zero K is about 58 % of that at the melting point for all the 10 fcc metals. The tabulated 4 equations (below and above the melting point/for fcc and liquid states) are provided for each of the 10 fcc metals. These equations will be useful for estimating phase equilibria of nano-materials.

AB - Approximated equations have been constructed to describe the temperature (T) dependence of the molar volumes (V) of fcc solid metals (Ag, Al, Au, Cu, Ir, Ni, Pb, Pd, Pt, and Rh) and their liquids below and above their melting points at standard pressure of 1 bar from zero Kelvin. Below the melting point, the following new approximated equation is suggested for both the solid and liquid metals: V = a + b * T (to the power of n), where a, b, and n are semi-empirical parameters (at n larger than 1; this equation obeys the boundary condition that the thermal expansion coefficient becomes zero at T = 0 K). This approximated equation reproduces the measured molar volume of solids from zero Kelvin to melting point with an accuracy of 0.2 % or better. As a compromise, the derivative of this equation reproduces the measured thermal expansion coefficient of solids only with an accuracy 10 % or better and only above 100 K. Above the melting point, the following well-known equation is used for both liquid and solid phases: V = c + d * T, where c and d are semi-empirical parameters. This equation implies that the thermal expansion coefficient above the melting point has an approximately constant value. It is found that the volume change upon melting extrapolated to zero K is about 58 % of that at the melting point for all the 10 fcc metals. The tabulated 4 equations (below and above the melting point/for fcc and liquid states) are provided for each of the 10 fcc metals. These equations will be useful for estimating phase equilibria of nano-materials.

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U2 - 10.1007/s10853-014-8627-z

DO - 10.1007/s10853-014-8627-z

M3 - Article

VL - 50

SP - 678

EP - 687

JO - Journal of Materials Science

JF - Journal of Materials Science

SN - 0022-2461

IS - 2

ER -